The safe and correct way to get an older version is contacting the developer. Maybe they will just give it to you or maybe not - there is a reason why they updated it in the first place. Most importantly they will want to know why and you won't get any hacked malware version as is possible from other sources.

Yeah they updated it so they could start charging for it, despite the old free version working perfectly fine.
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TriynkoJul 1 '14 at 20:30

Yeah, they updated it only so they could prompt the user with stupid KYC questions (banking) and pretend to comply with stupid laws that have total citizen surveillance, tracking and control as their objective. If I can say no to that kind of bullshitting I will. To do so, my only option at the moment is to keep the current app version or grab an old version from other sources (when "premium" and "trusted" Google Play service is incapable or unwilling to do so). Have the guts to say no and disobey when something is not right! Don't follow the stream of stupidification!
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sammygMay 22 at 11:06

While you are right about using trusted sources for installing apps onto ones phone, you must keep in mind that not all changes that are made to an app are for the good. Therefore, there are often very legitimate reasons why someone would want to hold onto an older version. At the very least, users should be given the choice! Not just the choice to update, but the choice to downgrade as well as keep current version. So called "developers" and companies like Google should not be just shoving new apps and versions down our throats, and we as users and consumers just taking it without a blink.
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sammygMay 22 at 11:12

You can't change the behavior of an app without the source code. So having only the APK is not enough. If someone wanted to, he could mask a malicious app as a legitimate one. So he could just use the name "bananas.apk" to make you think that it's that game that you love so much. That's one of the oldest tricks in the book. It's highly unlikely that it's the original app but with changed behavior. (With reservation for open source apps whose sources anyone can grab and change.) But if you want to be sure it's safe, just install it in an isolated environment, like a VM or a test phone.
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sammygMay 22 at 11:28